#### The Geometry of Origami

Discover the Geometry of Origami with Mathnasium!

Jun 4, 2024 | Point Loma

Mental math is a powerful tool that can transform the way you approach numbers. With a few tips and tricks, you can make arithmetic faster, more enjoyable, and even impress your friends. Here are some strategies to sharpen your mental math skills and make calculations a breeze.

- Break It Down: Decomposition

One of the most effective techniques in mental math is breaking numbers down into smaller, more manageable parts. This is known as decomposition. For instance, if you need to add 47 and 36, you can break it down like this: 47+36=(40+30)+(7+6)=70+13=83

By simplifying the numbers, you make the calculation much easier.

- Use Rounding and Compensating

Rounding numbers to the nearest ten can simplify calculations, especially for addition and subtraction. After rounding, you can compensate for the difference. For example: 68+24 Round 68 to 70 (add 2) and 24 to 20 (subtract 4). Then: 70+20=90 Now, adjust for the rounding: 90−2+4=92

This method works particularly well for multiplication as well. For instance: 49×6 Round 49 to 50, calculate: 50×6=300 Then subtract the excess: 300−6=294

- Utilize the Power of 10

The base-10 system is fundamental in mental math. Multiplying or dividing by 10, 100, or 1000 can often simplify problems. For example, to multiply 25 by 4: 25×4=100 This is because 25×4 is the same as (25×2)×2: 50×2=100

Similarly, for division, consider 180 by 5: 180÷5 You can multiply 180 by 2 to simplify the division: 180×2=360 Then divide by 10: 360÷10=36

- Master the Multiplication Tricks

Certain multiplication tricks can make your calculations swift. For example, to multiply by 9, you can use the fact that 10−1=9. For instance: 8×9=8×(10−1)=(8×10)−(8×1)=80−8=72

Another trick is the “finger method” for multiplying by 9. To multiply 7 by 9, hold up all ten fingers. Fold down the 7th finger from the left. You have 6 fingers on the left and 3 on the right, giving you 63.

- Square Numbers Ending in 5

Squaring numbers ending in 5 is straightforward. Consider 352: 352 Take the first digit (3) and multiply it by the next number (4): 3×4=12 Then, append 25: 352=1225

- Employ Cross Multiplication for 2-Digit Numbers

For quick multiplication of two 2-digit numbers, use cross multiplication. For example, 23×14: 23×14 Break it down into parts: (20+3)×(10+4) =20×10+20×4+3×10+3×4 =200+80+30+12 =322

By practicing these tips and tricks, mental math becomes less daunting and more intuitive. Over time, these strategies can significantly improve your speed and confidence in handling arithmetic, making math not just easier, but also a lot more fun.